Toward an Open-Access of High-Frequency Lake Modelling and Statistics Data for Scientists and Practitioners

Home , Lake Brienz, Lake Sempach

Toward an open-access of high-frequency lake modelling and statistics data for scientists and practitioners. The case of Swiss Lakes using Simstrat v2.1 Adrien Gaudard1†, Love Råman Vinnå1, Fabian Bärenbold1, Martin Schmid1, Damien Bouffard1 5 1Surface Waters Research and Management, Eawag, Swiss Federal Institute of Aquatic Sciences and Technology, Kastanienbaum, Switzerland † deceased, 2019 Correspondence to: Damien Bouffard ([email protected])

Abstract

10 One-dimensional hydrodynamic models are nowadays widely recognized as key tools for lake studies. They offer the possibility to analyse processes at high frequency, here referring to hourly time scale, to investigate scenarios and test hypotheses. Yet, simulation outputs are mainly used by the modellers themselves and often not easily reachable for the outside community. We have developed an open-access web-based platform for visualization and promotion of easy access to lake model output data updated in near real time (simstrat.eawag.ch). This platform was developed for 54 lakes in Switzerland with 15 potential for adaptation to other regions or at global scale using appropriate forcing input data. The benefit of this data platform is practically illustrated with two examples. First, we show that the output data allows for assessing the long term effects of past climate change on the thermal structure of a lake. The study confirms the need to not only evaluate changes in all atmospheric forcing but also changes in the watershed or through-flow heat energy and changes in light penetration to assess the lake thermal structure. Then, we show how the data platform can be used to study and compare the role of episodic strong 20 wind events for different lakes on a regional scale and especially how their thermal structure is temporarily destabilized. With this open-access data platform we demonstrate a new path forward for scientists and practitioners promoting a cross-exchange of expertise through openly sharing of in-situ and model data.

1 Introduction

Aquatic research is particularly oriented towards providing relevant tools and expertise for practitioners. Understanding and monitoring inland waters is often based on in situ observations. Today, the physical and biogeochemical properties of many lakes are monitored using monthly to bi-monthly vertical discrete profiles. Yet, part of the dynamics is not captured at this 5 temporal scale (Kiefer et al., 2015). An emerging alternative approach consists in deploying long-term moorings with sensors and loggers at different depths of the water column. However, this approach is seldom used for country-level monitoring, although it is promoted by research initiatives such as GLEON (Hamilton et al., 2015) or NETLAKE (Jennings et al., 2017).

It is common to parameterize aquatic physical processes with mechanistic models, and ultimately use them to understand aquatic systems through scenario investigation or projection of trends in for example a climate setting. In the last decades, 10 many lake models have been developed. They often successfully reproduce the thermal structure of natural lakes (Bruce et al., 2018). Today’s most widely referenced one-dimensional (1D) models include (alphabetic order) DYRESM (Antenucci and Imerito, 2000), FLake (Mironov, 2005), GLM (Hipsey et al., 2014), GOTM (Burchard et al., 1999), LAKE (Stepanenko et al., 2016), Minlake (Riley and Stefan, 1988), MyLake (Saloranta and Andersen, 2007), and Simstrat (Goudsmit et al., 2002). The results from these models are mainly used by the modellers themselves, and often not easily accessible for the outside 15 community.

The performance of lake models is determined by the physical representativeness of the algorithms and by the quality of the input data. The latter include (i) lake morphology, (ii) atmospheric forcing, (iii) hydrological cycle (e.g. inflow, outflow and/or water level fluctuations), and (iv) light absorption. In situ observations, such as temperature profiles, are required for calibration of model parameters. To support this approach, it is important to promote and facilitate the sharing of existing 20 datasets of observations among scientists and practitioners. Conversely, scientists and practitioners should benefit from the model output, which is often ready-to-use, high-frequency and up-to-date. Yet, model output data should not only be seen as a tool for temporal interpolation of measurements. Models also provide data of hard to measure quantities which are helpful for specific analyses (e.g., the heat content change to assess impact of climate change, or the vertical diffusivity to estimate vertical turbulent transport). Models finally support the interpretation of biogeochemical processes which often depend on the 25 thermal stratification, mixing and temperature. In a global context of open science, collaboration between the different actors and reuse of field and model output data should be fostered. Such win-win collaboration serves the interests of lake modellers, researchers, field scientists, lake managers, lake users, and the public in general.

In this work, we present a new automated web-based platform to visualize and distribute the near real time (weakly) output of the one-dimensional hydrodynamic lake model Simstrat through an user-friendly web interface. The current version includes 30 54 Swiss lakes covering a wide range of characteristics from very small volume such as Inkwilersee (9 x 10-3 km3) to very large systems such as Lake Geneva (89 km3), over an altitudinal gradient (Lago Maggiore at from 193 m. a.s.l. to Daubensee at 2207 m. a.s.l.) and over all trophic states (14 euthrophic lakes, 10 mesotrophic lakes and 21 oligotrophic lakes, Appendix

A). We focus here on describing the fully automated workflow, which simulates the thermal structure of the lakes and weekly updates the online platform (https://simstrat.eawag.ch) with metadata, plots and downloadable results. This state-of-the-art framework is not restricted to the currently selected lakes and can be applied to other systems or at global scale.

2 Methods

5 2.1 Model and workflow

We use the 1D lake model Simstrat v2.1 to model 54 Swiss lakes or reservoirs (see Appendix A for details of modelled lakes) in an automated way. Simstrat was first introduced by Goudsmit et al. (2002) and has been successfully applied to a number of lakes (Gaudard et al., 2017; Perroud et al., 2009; Råman Vinnå et al., 2018; Schwefel et al., 2016; Thiery et al., 2014). Recently, large parts of the code were refactored using the object-oriented Fortran 2003 standard. This version of Simstrat 10 provides a clear, modular code structure. The source code of Simstrat v2.1 is available via GitHub at: https://github.com/Eawag-AppliedSystemAnalysis/Simstrat/releases/tag/v2.1. A simpler build procedure was implemented using a docker container. This portable build environment contains all necessary software dependencies for the build process of Simstrat. It can therefore be used on both Windows and Linux systems. A step-by-step guide is provided on GitHub.

In addition to the improvements already described by Schmid and Köster (2016), Simstrat v2.1 includes (i) the possibility to 15 use gravity-driven inflow and a wind drag coefficient varying with wind speed – both described by Gaudard et al. (2017), and (ii) an ice and snow module. The ice and snow module employed in the model is based on the work of Leppäranta (2014, 2010) and Saloranta and Andersen (2007), and is further described in Appendix B.

A Python script was developed to (i) retrieve the newest forcing data directly from data providers and integrate them into the existing datasets, (ii) process the input data and prepare the full model and calibration setups, (iii) run the calibration of the 20 model for the chosen model parameters, (iv) provide output results, and (v) update the simstrat.eawag.ch online data platform to display these results. The script is controlled by an input file written in JSON format, which specifies the lakes to be modelled together with their physical properties (depth, volume, bathymetry, etc.) and identifies the meteorological and hydrological stations to be used for model forcing. The overall workflow is illustrated in Figure 1.

2.2 Input data

25 Table 1 summarizes the type and sources of the data fed to Simstrat. For meteorological forcing, homogenized hourly air temperature, wind speed and direction, solar radiation and relative humidity from the Federal Office of Meteorology and Climatology (MeteoSwiss, CH) weather stations are used. For each lake the closest weather stations are used. Air temperature is corrected for the small altitude difference (see Appendix A) between the lake and the meteorological station, assuming an adiabatic lapse rate of -0.0065 °C m-1. This correction is a source of error in high altitude lakes like Daubensee for which 30 dedicated meteorological station would be needed. The cloud cover needed for downwelling longwave radiations are estimated 3

by comparing observed and theoretical solar radiation (Appendix C). For hydrological forcing, homogenized hourly data from the stations operated by the Federal Office for the Environment (FOEN) are used. For each lake, the data from the available stations at the inflows are aggregated to feed the model with a single inflow. The aggregated discharge is the sum of the discharge of all inflows, and the aggregated temperature is the weighted average of the inflows for which temperature is 5 measured. Inflow data are often missing for small or high altitude lakes (Appendix A). Missing inflows and more generally watershed data is a source of error in small alpine lakes, yet, such error can be compensated during the calibration process. The light absorption coefficient [m-1] is either obtained from Secchi depth [m] measurements (for Inkwilersee,

Lake Biel, Lake Brienz, Lake Geneva,𝜀𝜀abs Lake Neuchatel, Lower Lake Zurich, Oeschinensee,𝑧𝑧Secchi Upper Lake Constance, and Sihlsee), or is set to a constant value based on the lake trophic status. In the first case, the following equation is applied: =

-1 10 1.7/ (Poole and Atkins, 1929, Schwefel et al. 2016). In the second case, is set to 0.15 m for oligotrophic𝜀𝜀 lakes,abs -1 -1 0.25 𝑧𝑧mSecchi for mesotrophic lakes, and 0.50 m for eutrophic lakes. The values correspond𝜀𝜀abs to observations of Secchi depths in Swiss lakes (Schwefel et al. 2016) and fall into the decreasing range of transparency from an oligotrophic to eutrophic system (Carlson 1977). For glacier-fed lakes (typical above 2000 m) rich in sedimentary material, is set to 1.00 m-1.

abs The timeframe of the model is determined by the availability of the meteorological data𝜀𝜀 (air temperature, solar radiation, 15 humidity, wind, precipitation). Initial conditions for temperature and salinity are set using conductivity-temperature-depth (CTD) profiles or using the temperature information from the closest lake. We apply different data patching methods to remove data gaps from the forcing depending on the length of the data gap. For small data gaps with duration not exceeding one day, the dataset is linearly interpolated. In total < 1 % of the dataset is corrected using this approach. Longer data gaps of up to 20 days are replaced by the long-term average values for the corresponding day of the year. Only ~ 1.5 % of the dataset is corrected 20 using this approach.

2.3 Calibration

Model parameters are set to default values, and four of them are calibrated (see Table 2). The parameters p_radin and and f_wind scale the incoming long-wave radiation and the wind speed, respectively, and can be used to compensate for systematic differences between the meteorological conditions on the lake and at the closest meteorological station. The parameter a_seiche 25 determines the fraction of wind energy that feeds the internal seiches. This parameter is lake-specific, as it depends on the lake’s morphology and it's exposition to different wind directions. Finally, the parameter p_albedo scales the albedo of ice and snow applied to incoming shortwave radiation, which depends on the ice/snow cover properties. The calibration parameters were selected according to their importance for the model (e.g. based on previous sensitivity analysis), and their number was deliberately kept small in order to keep the calibration process simple and focused. Calibration is performed using PEST v15.0 30 (see http://pesthomepage.org), a model-independent parameter estimation software (Doherty, 2016). As a reference for calibration, temperature observations from CTD profiles are used. Calibration is performed on a yearly basis, unless significant changes are made to either the model, the forcing data, or the observational data (e.g. release of a new version of Simstrat or 4

delivery of a large amount of new observational data). For the eight lakes without observational data, parameters are set to their default value (see Table 2) with no calibration performed, and the lack of calibration is indicated on the online platform.

2.4 Output / Available data on the online platform

The online platform (accessible at https://simstrat.eawag.ch) is automatically fed every week with model results, metadata and 5 plots for all the 54 modelled lakes (see Figure 2). It allows for efficient display and open sharing of the model results for interested users. While the framework is here restricted to Swiss lakes, the code could be easily adapted to other lakes outside Switzerland and used at the global scale. From the model results, we directly obtain time series of several model output variables. Those dataset include temperature, salinity, Brunt-Väisälä frequency, vertical diffusivity, and ice thickness. In addition, we use the following known physical and lake-related properties: the acceleration of gravity = 9.81 m2 s-1, the heat

-1 -1 3 2 10 capacity of water = 4.18 10 J K kg , the volume of the lake [m ], the area [m ], temperature𝑔𝑔 [°C], and density 3 [kg m-3] at depth𝑐𝑐p [m], and∙ the mean lake depth = 𝑉𝑉 [m] to calculate𝐴𝐴 𝑧𝑧time series of derived𝑇𝑇𝑧𝑧 values: 1 𝜌𝜌𝑧𝑧 𝑧𝑧 𝑧𝑧̅ 𝑉𝑉 ∫ 𝑧𝑧 𝐴𝐴𝑧𝑧 𝑑𝑑𝑑𝑑 • Mean lake temperature: = [°C] 1 • Heat content: = 𝑧𝑧 [J]𝑧𝑧 𝑇𝑇� 𝑉𝑉 ∫ 𝑇𝑇 𝐴𝐴 𝑑𝑑𝑑𝑑 -2 • Schmidt stability: p= 𝑧𝑧 𝑧𝑧( 𝑧𝑧 ) [J m ] 𝐻𝐻 𝑐𝑐 ∫ 𝜌𝜌𝑔𝑔 𝑇𝑇 𝐴𝐴 𝑑𝑑𝑑𝑑 15 • Timing of summer𝑆𝑆 Tstratification:𝐴𝐴0 ∫ 𝑧𝑧 − 𝑧𝑧we̅ 𝜌𝜌 use𝑧𝑧 𝐴𝐴𝑧𝑧 a𝑑𝑑 threshold𝑑𝑑 based on the Schmidt stability to determine beginning and end of summer stratification. The lake is assumed to be stratified for / 10 J m-3. Using a different criterion (e.g., temperature difference between surface and bottom water) results in variations in the calculated stratification period; 𝑆𝑆𝑇𝑇 𝑧𝑧𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 ≥ however, the general pattern among lakes remains similar. • Timing of ice cover: we use the existence of ice to determine beginning and end of ice covered period.

20 From these results, we create static and interactive plots. The latter are created using the Plotly Python Library (see https://plot.ly/python). The plots can be categorized as follows:

• History (e.g., contour plot of the whole temperature time series, line plot of the whole time series of Schmidt stability); • Current situation (e.g., latest temperature profile); • Statistics (e.g., average monthly temperature profiles, long-term trends).

25 All Output and processed data are directly available from the online platform.

3 Results and discussion

Analysis of model output allows to compare the response of the different systems to specific events or to long term changes. The Simstrat model web interface provides regional long-term high-frequency data updated in near real-time as output. This represents a novel way to monitor, analyse and visualize processes in aquatic systems, and, most importantly, grant the entire 30 community direct access to the findings. The coupling between Simstrat and PEST provides an effective way to calibrate model parameters. The uncertainty quantification finally allows an appropriate informed use of the output data. Yet, more 5

advanced methods for both parameter estimation and uncertainty quantification such as Bayesian inference (Gelman et al., 2013) should be applied to Simstrat.

Out of the 46 calibrated lakes, the post-calibration root mean square error (RMSE) is < 1 °C for 17 lakes, between 1 and 1.5 °C for 15 lakes, between 1.5 and 2 °C for 8 lakes and between 2 °C and 3°C for 6 lakes (Figure 3). There were too few in-situ 5 observations on 8 lakes to perform a proper calibration and all parameters where thereby set to default values. Overall, the performance is comparable to the RMSE range of ~0.7-2.1 °C reported in a recent global 32-lake modelling study using GLM (Bruce et al., 2018) also including Lake Geneva, Lake Constance and Lake Zurich. The correlation coefficient remains always higher than 0.93 suggesting also that the model successfully reproduce the thermal structure of the investigated lakes Overall, the quality of the results is better for lowland lakes than for high altitude lakes where local meteorological and watershed 10 information are often missing.

We illustrate the potential of high-frequency lake model data with two examples: first by briefly showing the long-term changes caused by climate change in Lake Brienz (section 3.1), and secondly by investigating the differential response of lakes across Switzerland to episodic forcing (short-term extremes, section 3.2).

3.1 Long-term evolution of the thermal structure of lakes in response to climate trends

15 Over the period 1981–2015, yearly averaged simulated surface temperatures in Lake Brienz increased with a significant (p<0.001) trend of +0.69 °C/decade (Figure 4a). For the same period, monthly in situ observations indicate a similar trend of 0.72 °C/decade (p~0.07), while the trend of air temperature at the meteorological station in Interlaken is lower (+0.50 °C/decade, p<0.01). Based on physical principles, lake surface temperature is expected to increase less than air temperature (Schmid et al., 2014), however Schmid and Köster (2016) also observed a higher trend in lake surface temperature than in air 20 temperature for Lower Lake Zurich and assigned the excess warming to a positive trend in solar radiation. For the period 1981- 2015, the ascending trend in solar radiation is 5 W/m2/decade that corresponds to an equilibrium temperature increase of about 0.2°C/decade. The warming rate at the surface of Lake Brienz is larger than observed trends in neighbouring lakes with reported increases of +0.46 °C/decade for Upper Lake Constance (1984 – 2011, Fink et al. 2014), +0.41°C/decade for Lower Lake Zürich (1981 - 2013, Schmid and Köster, 2016; 1955 - 2013, Livingstone, 2003), +0.55°C/decade for Lower Lake Lugano 25 (1972 – 2013, Lepori and Roberts, 2015). This can be explained by the lower light penetration in Lake Brienz (ranging from ~1 m to ~10 m) compared to other lakes; the increase in solar radiation being distributed into a shallower layer and thereby warming slightly more the lake surface.

The temperature increase was significantly smaller in the hypolimnion, with a minimum trend at the lake bottom of 0.16 °C/decade (p<0.001), leading to a depth-averaged rate of temperature increase of 0.22 °C/decade (p<0.001). The temperature 30 difference between the inflow and the outflow also contributes to the heat budget. While no significant change in the yearly total discharge was observed at the gauging stations of FOEN for the inflows of the Aare and of the Lütschine rivers for the

period 1981 – 2015, the weighted inflow temperature increased by 0.26 °C/decade. The riverine temperature remains colder than the lake surface temperature leading to a yearly average loss of energy by through-flow of ~ - 40 W/m2 for 2015. This result is consistent with the recent observations of Råman Vinnå (2018) suggesting that tributaries significantly affect the thermal response of lakes with residence time up to 2.7 years (as Lake Brienz). The contribution of the river to the heat budget 5 of Lake Brienz is also ~ 4 times larger than that previously estimated for Upper Lake Constance (Fink et al. 1994), a lake with a longer residence time. The increasing difference over time between the inflow temperature and the outflow temperature (taken as the lake surface temperature) leads to a non-negligible cooling contribution from the river of ~ 0.14 °C/decade (p<0.05). The temporal change in the discharge and its temperature resulting from climate change should therefore be taken into account in studies attempting to predict the change in lake thermal structure.

10 The vertically heterogeneous warming modelled in Lake Brienz is consistent with previous observations showing that the difference in warming between the surface and the bottom increases the strength and duration of the stratified period (Zhong et al., 2016; Wahl and Peeters, 2014). We simulate an earlier onset of the stratification in spring of -7.5 day/decade (p<0.001) and a later breakdown of the stratification by +3.7 day/decade (p<0.001) (Figure 4c). Both the warming trend and the increase in length of the stratified period increase the Schmid stability (Figure 4d) and heat content (Figure 4f). Finally, the yearly 15 maximum stratification strength (Brunt-Väisälä frequency, Figure 4e) gradual increases over the investigated period with a rate of 3.3 x 10-4 s-2/decade. The simulated increase in overall stability (Figures 4d, 4e and 4f) reduces vertical mixing and affects the vertical storage of heat with less heat transferred immediately below the thermocline causing a slight decrease in temperature observed in autumn at ~30 m depth (Figure 4b). This effect is even more clearly seen in other lakes like Lake Geneva ( https://simstrat.eawag.ch/LakeGeneva) with the surface waters warming strongly (+1 °C/decade in June), resulting 20 in a cooling layer between 20 and 60 m (-0.2 °C/decade) in late summer. Such a reduction of vertical exchange is self- strengthening and enhances the differential vertical warming.

Such analyses can be extended to all modelled lakes. An inter-comparison of the temporal extent of summer stratification and winter ice cover period is illustrated in Figure 5. An altitude-dependent decrease of the duration of summer stratification is observed, along with a stronger corresponding increase in the duration of the inverse winter stratification from 1200 m. a.s.l. 25 This is possibly linked to an altitude dependency of climate-driven warming in Swiss lakes, first reported by Livingstone et al. (2005), which may be caused by a delay in meltwater runoff (Sadro et al., 2018). Here this process is not directly resolved but incorporated through the calibration procedure spanning all seasons.

In conclusion, the online platform provides all the data to estimate the past warming rate of lakes and evaluate how the different external processes contribute to their heat budgets. The change in the thermal structure depends mostly on the change in 30 atmospheric forcing, yet, other factors such as the changes in discharge and temperature from the tributaries and the light absorption into the lake should also be taken into account. We specifically show that the warming rate of the lake surface temperature significantly differs from that of depth-averaged temperature, thereby highlighting the benefit of using either in-

situ observations resolving the thermal structure over the water column or hydrodynamic model output for assessing climate change impacts on lake thermal structure.

3.2 Event based evolution of the lake thermal structure.

A major drawback of traditional lake monitoring programs in Switzerland is the coarse temporal resolution, with measurements 5 often performed on a monthly basis. Thought sufficient for direct long-term trend studies as shown in section 3.1 when conducted over an extended period typically longer than 30 years (Gray et al., 2018). However, traditional monitoring programs cannot resolve the impact of short-term events and their consequences for the ecosystem. This is a strength of high- frequency (hourly time scale) lake modelling, which allows for simulation and comparison of the effects associated with rapid and often severe events such as storms. Based on high-frequency observations, Woolway et al. (2018) showed the effects of a 10 major storm on Lake Windermere. They observed a decrease in the strength of the stratification, a deepening of the thermocline and the onset of internal waves oscillations ultimately upwelling oxygen depleted cold water into the downstream river. Furthermore, Perga et al. (2018) illustrated how storms could be just as important as gradual long-term trends for changes in light penetration and thermal structure in an Alpine lake.

Here we demonstrate how high-frequency model output can be used to study the influence of specific events on the thermal 15 dynamics of lakes. As an example, we focus on the 28th of June 2018 when Switzerland experienced a strong but by no means exceptional storm with Northeasterly winds mainly affecting the North-Western part of the country – the mean wind speed during that day is shown spatially in Figure 6a. The evolution of the stratification strength, illustrated here by the Schmidt stability, is given in Figure 6b for one of the most affected lakes, Lake Neuchâtel (https://simstrat.eawag.ch/LakeNeuchatel, Figure 2). This lake, with the main axis well-aligned to synoptical winds, experienced a ~8 % decrease in the Schmidt stability 20 over this half-day event. Yet, the effects were not long-lasting and the Schmidt stability reverted to its pre-storm value within ~5 days (Figure 6b). This also resulted in a total increase of the lake heat content by ~1.4·1016 J from the start of the storm to the time of recovery. We used the Schmidt stability recovery duration as a way to assess the short-term effect of the storm on the different modelled lakes. In Figure 6a, lakes are coloured based on the delay in Schmidt stability increase (in days) caused by the storm. The impact of the storm was not limited to Lake Neuchâtel but rather showed a regionally-varying pattern. 25 Particularly small- to medium-sized lakes in the North-Western parts of Switzerland were more affected than large lakes or lakes located in the Southern part of Switzerland. However, the thermal structure of these lakes quickly reverted to the seasonal early summer warming trend.

So far, climate-driven warming has been recognized to cause an overall increase in lake stratification strength and duration, and a gradual warming of the different layers (Schwefel et al., 2016; Zhong et al., 2016; Wahl and Peeters, 2014). Air 30 temperature trend was the most studied forcing parameter. Yet, the dynamics of extreme events (such as heat waves, drought spells, storms), including their changes in strength and distribution, has been comparatively overlooked. Scenario exploration,

climate change studies, or historical forcing reanalysis should be integrated in such web-based hydrodynamic platforms to assess their roles in modifying the lake thermal structures and heat storage.

4 Conclusion

The workflow presented in this paper allows openly sharing of high-frequency, up-to-date and permanently available lake 5 model results for multiple users and purposes. We demonstrated the benefit of the platform through two simple case studies. First, we showed that the high frequency modelled temperature data allows a complete assessment of the effect of climate change on the thermal structure of a lake. We specifically show the need to evaluate changes in all atmospheric forcing, in the watershed or through-flow heat energy and in light penetration to accurately assess the evolution of the lake thermal structure. Then we showed that the high frequency modelled data can be used to investigate special events such as wind storms, there 10 in-situ measurements under current temporal resolution are failing. More generally, these results are well suited for the following applications and target groups:

• For the public, the platform serves as an informative website enabling easy access to broad quantities of regional scientific results, with the intention of raising interest about lake ecosystem dynamics. • For lake managers, the platform makes relevant information available, such as (i) near real time temperature and 15 stratification conditions of the lakes, (ii) simple statistical analyses such as monthly temperature profiles and long- term temperature trends. • For researchers, this work can facilitate (i) scenario modelling of any of the lakes, as the basic model setup is ready- to-use, (ii) improvement of the lake model with addition of previously unresolved processes (e.g., resuspension with changed light properties), (iii) access to variables that were previously not or irregularly available (e.g., vertical 20 diffusivity, heat content, stratification and heat fluxes), and (iv) specific comparative analyses, whereby a given question can be investigated simultaneously over many lakes (e.g., the impact of climate change or a regional storm).

By promoting a cross-exchange of expertise through openly sharing of in-situ and model data at high frequency, this open- access data platform is a new path forward for scientists and practitioners.

25 Code and data availability

The workflow was developed for Swiss lakes but can be easily extended to other geographical area or at global scale by using other meteorological input data. Simstrat and the Python workflow are available on https://github.com/Eawag- AppliedSystemAnalysis/Simstrat/releases/tag/v2.1 (https://doi.org/10.5281/zenodo.2600709) and https://github.com/Eawag- AppliedSystemAnalysis/Simstrat-WorkflowModellingSwissLakes (https://doi.org/10.5281/zenodo.2607153). Meteorological

data are available from MeteoSwiss (https://gate.meteoswiss.ch/idaweb/), hydrological data are available from FOEN (https://www.hydrodaten.admin.ch), CTD data were provided by various sources listed here: https://simstrat.eawag.ch/impressum . The calibration software PEST is available on http://www.pesthomepage.org/

Author contribution

5 The new version of Simstrat was developed by FB, AG and LRV. The workflow was developed by AG. The ice model was developed by LVR. The concept of the workflow was defined by DB. All authors contributed to the validation of the model and interpretation of the results. AG and DB wrote the manuscript with contributions from FB, LVR and MS.

Competing interests

The authors declare that they have no conflict of interest

10 Acknowledgment

We thank Davide Vanzo for helping with the Docker and the scripts and Michael Pantic for helping restructuring the version 2.1 of Simstrat. We finally thank Marie-Elodie Perga for her comments on a preliminary version of the manuscript. The full list of acknowledgements regarding in-situ observations can be found here: https://simstrat.eawag.ch/impressum .

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Figure 1. General workflow diagram. Model input (left box) is retrieved and processed by the Python script “Simstrat.py”, which runs the model (Simstrat v2.1) and/or model calibration (using PEST v15.0) and produces output (right box). This output is then 5 uploaded to a web interface (https://simstrat.eawag.ch) for general use. All scripts and programs are available on https://github.com/Eawag-AppliedSystemAnalysis/Simstrat/releases/tag/v2.1 and https://github.com/Eawag- AppliedSystemAnalysis/Simstrat-WorkflowModellingSwissLakes. Simstrat = one dimensional hydrodynamic model; CTD = Conductivity, Temperature, Depth profiler; PEST = Model independent parameter estimation and uncertainty analysis software; FOEN = Swiss Federal Office of Environment; MeteoSwiss = Swiss Federal Office of Meteorology and Climatology; Swisstopo = 10 Swiss Federal Office of Topography

5 Figure 2. Illustration of the interactive map displayed on the homepage of the online platform: https://simstrat.eawag.ch. The location of the lakes discussed in this manuscript is also indicated with numbers (See Appendix A). Basemap is provided by Swisstopo and the specific legend can be found here https://api3.geo.admin.ch/static/images/legends/ch.swisstopo.swisstlm3d-karte- farbe_en_big.pdf

Figure 3. Performance of the model for the different lakes, as shown by the root mean square error (RMSE) and the correlation coefficient. Six lakes (with symbol o on the legend) with RMSE > 2 °C are not shown.

Figure 4. Evolution of several indicators for Lake Brienz over the period 1981-2018; all linear regression have p_values << 0.001: (a) yearly mean lake surface temperature (0.69 °C/decade), yearly mean air temperatures (0.49 °C/decade), yearly mean tributary temperatures (0.26 °C/decade), yearly mean lake temperatures (0.22 °C/decade) and yearly mean bottom temperatures (0.16 5 °C/decade), with linear regression, (b) contour plot of the linear temperature trend through depth and month, (c) yearly start (+3.7 days/decade) and end (-7.5 days/decade) day of summer stratification, with linear regression, (d) yearly mean (line), min and max (shaded area) Schmidt stability, with linear regression, (e) yearly maximum Brunt-Väisälä frequency (3.3x10-4 1/s2/decade), with linear regression (f) yearly mean (line), min and max (shaded area) heat content.

Figure 5. Comparison of timing of stratification and ice cover for the considered lakes. The coloured areas represent the mean periods of summer stratification (red) and ice cover (blue); the vertical lines represent the last year (here, 2017). The transparency for the ice cover indicates the freezing frequency: full transparency means that ice was never modelled, while no transparency means 5 that ice was modelled every winter. Lakes are ordered from left (low elevation) to right (high elevation). The time period of data used is indicated in Appendix A.

Figure 6. (a) Mean wind field on June 28th, 2018 (data source: MeteoSwiss, COSMO-1 model, coordinate system CH1903+) and delay in Schmidt stability increase for the modelled lakes: from no delay (white) to a delay of more than 5 days (red). (b) Schmidt stability (daily average) in Lake Neuchâtel during the period of the storm.

Table 1. Input data sources used for the model Data Source Model input

Lake bathymetry Swisstopo Bathymetry profile

(https://www.swisstopo.admin.ch)

Meteorological MeteoSwiss Air temperature, solar radiation, forcing humidity, wind, cloud cover, (http://meteoswiss.admin.ch) precipitation

Hydrological forcing FOEN Inflow discharge, inflow temperature

(http://hydrodaten.admin.ch)

Secchi depth Eawag, cantonal monitoring Light absorption coefficient

CTD profiles Eawag, cantonal monitoring Initial conditions, temperature observations for calibration

Table 2. Model parameters. The asterisk (*) indicates the parameters that were calibrated. The geothermal heat flux is based on existing geothermal data for Switzerland: https://www.geocat.ch/geonetwork/srv/eng/md.viewer#/full_view/2d8174b2-8c4a-44ea- b470-cb3f216b90d1. Parameter Description and units Default value

lat Latitude [°] Based on lake location

p_air Air pressure [mbar] Based on lake elevation

a_seiche* Ratio of wind energy going into seiche energy [-] Based on lake size

q_nn Fractionation coefficient for seiche energy [-] 1.10

f_wind* Scaling factor for wind speed [-] 1.00

c10 Scaling factor for the wind drag coefficient [-] 1.00

cd Bottom drag coefficient [-] 0.002

hgeo Geothermal heat flux [W/m2] Based on geothermal map (see table caption)

p_radin* Scaling factor for the incoming long wave radiation [-] 1.00

p_windf Scaling factor for the fluxes of sensible and latent heat 1.00 [-]

albsw Albedo of water for short wave radiation [-] 0.09

beta_sol Fraction of short wave radiation absorbed as heat in the 0.35 uppermost water layer [-]

p_albedo* Scaling factor for snow/ice albedo, thereby affecting 1.00 melting and under ice warming [-]

freez_temp Water freezing temperature [°C] 0.01

snow_temp Temperature below which precipitation falls as snow 2.00 [°C]

Appendix

A. Properties of the modelled lakes The following table summarizes the main properties of the 54 lakes we model in this work. The full dataset is available as a JSON file. An asterisk after the lake name indicates that this lake was not calibrated due to the lack of observational data. 5 MeteoSwiss = (Swiss) Federal Office of Meteorology and Climatology. FOEN = (Swiss) Federal Office for the Environment. # indicates lakes where secchi disk depth are available. For lakes with clearly defined multi basin such as Lake Lucerne, Lake Zurich, Lake Constance and Lake Lugano, each basin is considered as a separated lake connected to the other basins by inflows/outflows

Lake Volume Surface Max Retention Elevation Trophic Weather Hydrological Model [km3] [km2] depth [m] time [y] [m] state station IDs station IDs timeframe (MeteoSwiss) (FOEN)

Lake Aegeri 1 0.36 7.3 83 ~ 6.8 724 O AEG, SAG, - 2012-2018 EIN 689574 / 191747

Lake Baldegg 2 0.174 5.2 66 ~ 4.2 463 E MOA - 2012-2018

662239 / 228077

Lake Hallwil 3 0.285 10.3 48 ~ 3.9 449 E MOA 2416 2012-2018

658779 / 237484

Lake Biel 4 1.12 39.3 74 ~ 0.16 429 E# CRM 2085, 2307, 1993-2018 2446 578599 / 214194

Upper Lake 5 47.6 473 251 ~ 4.3 395 M# ARH, GUT 2473, 2308, 1981-2018 Constance 2312

749649 / 275225

Lower Lake 6 0.8 63 45 ~ 0.05 395 M STK, HAI, - 1981-2018 Constance GUT

718479 / 285390

Lake Brienz 7 5.17 29.8 259 ~ 2.7 564 O# INT 2019, 2109 1981-2018

640709 / 175275

Lake Thun 8 6.5 48.3 217 ~ 1.9 558 O# THU, INT 2457, 2469, 1981-2018 2488 619899 / 172630

Lake Geneva 9 89 580 309 ~ 11 372 M# PUY 2009, 2432, 1981-2018 2433, 2486, 533600 / 2493 144624

Greifensee 10 0.15 8.5 32 ~ 1.1 435 E SMA - 1981-2018

693699 / 245032

Lac de la 11 0.22 9.6 75 ~ 0.4 677 NA MAS, GRA 2160, 2412 2011-2018 Gruyère

573990 / 168654

Klöntalersee 12 0.056 3.3 45 ~ 0.5 848 O GLA - 1981-2018

716984 / 209627

Lac de Joux 13 0.145 8.77 32 0.85 1004 M CHB, BIE - 2009-2018

511590 / 165965

Lago di 14 0.1 1.68 204 A 470 O OTL 2605 1981-2018 Vogorno*

709279 / 118833

Lake Maggiore 15 37 212 372 ~ 4 193 O OTL 2068, 2368 1981-2018

694300 / 92576

Upper Lake 16 4.69 27.5 288 ~12.3 271 E LUG 2321 1981-2018 Lugano

721139 / 95471

Lower Lake 17 1.14 20.3 95 ~ 1.4 271 M LUG 2629, 2461 1981-2018 Lugano

714239 / 86391

Lake Lungern 18 0.065 2 68 ~ 0.6 688 NA GIH - 2010-2018

655099 / 183325

Lake Murten 19 0.55 22.8 45 ~ 1.2 429 M# NEU 2034 1981-2018

572700 / 198094

Lake Neuchâtel 20 13.8 218 152 ~ 8.2 429 M# NEU 2378, 2369, 1981-2018 2480, 2458, 554800 / 2447 194974

Lake Pfäffikon 21 0.059 3.3 36 ~ 2.1 537 M SMA - 1981-2018

701604 / 245377

Lake Sempach 22 0.66 14.5 87 ~ 16.9 504 M EGO 2608 2010-2018

654629 / 221355

Lake Sarnen 23 0.239 7.5 51 ~ 0.8 469 O GIH - 2010-2018

658349 / 190767

Lake Lucerne: 24 0.1 4.5 35 ~ 0.3 434 O LUZ 2102, 2436 1981-2018 Alpnachersee

667144 / 202267

Lake Lucerne: 25 3.16 22 200 ~ 2.0 434 O ALT 2056, 2276 1981-2018 Urnersee

688649 / 200895

Lake Lucerne: 26 4.41 30 214 ~ 1.6 434 O GES, ALT 2084, 2481 1981-2018 Gersauer- and Treibbecken

681659 / 203585

Lake Lucerne: 27 4.35 59 151 ~ 0.7 434 O LUZ - 1981-2018 Kreuztrichter and Vitznauerbecken

672049 / 208875

Walensee 28 2.5 24.2 151 ~ 1.4 419 O QUI, LAC, 2372, 2426 1981-2018 GLA 735739 / 202690

Lake Zug 29 3.2 38.3 197 ~ 14.7 417 E CHZ, WAE 2477 1981-2018

680049 / 216865

Sihlsee 30 0.096 11.3 22 ~ 0.4 889 O EIN 2300, 2635 2012-2018

701504 / 222387

Wägitalersee* 31 0.15 4.18 65 ~ 1.6 900 O LAC, EIN - 2012-2018

701504 / 222387

Upper Lake 32 0.47 20.3 48 ~ 0.69 406 M WAE 2104 1981-2018 Zurich

707159 / 229595

Lower Lake 33 3.36 68.2 136 ~ 1.4 406 M# LAC, SCM, - 1981-2018 Zurich WAE

687209 / 237715

Lago di 34 0.12 1.98 85 ~ 0.5 962 O ROB 2078 1981-2018 Poschiavo

804706 / 128871

Lake Sils 35 0.137 4.1 71 ~ 2.2 1797 O SIA - 2014-2018

776533 / 143922

Lake Silvaplana 36 0.14 2.7 77 ~ 0.7 1791 O SIA - 2014-2018

780801 / 146926

Lake St. Moritz 37 0.02 0.78 44 ~ 0.1 1768 O SAM 2105 1981-2018

784870 / 152099

Lake Lauerz 38 0.0234 3.07 14 ~ 0.3 447 M GES, LUZ - 1981-2018

688864 / 209546

Rotsee 39 0.00381 0.48 16 ~ 0.4 419 E LUZ - 1981-2018

666491 / 213558

Daubensee* 40 0.64 50 NA 2207 O BLA - 2013-2018

613862 / 140026

Lej da Vadret* 41 0.43 50 NA 2160 O SIA - 2014-2018

785308 / 141515

Lake Davos* 42 0.0156 0.59 54 NA 1558 O DAV - 1981-2018

784261 / 188317

Lac de 43 0.0532 1.6 105 NA 1250 O CHD - 2012-2018 l'Hongrin*

569975 / 141537

Türlersee 44 0.00649 0.497 22 ~ 2 643 E WAE - 1981-2018

680514 / 235858

Amsoldingersee 45 0.00255 0.382 14 NA 641 E# THU - 2012-2018

610534 / 174906

Lac Noir* 46 0.00252 0.47 10 NA 1045 M PLF - 1989-2018

587970 / 168280

Moossee 47 0.00339 0.31 21 NA 521 E BER - 1981-2018

603165 / 207928

Mauensee 48 0.55 9 NA 504 E EGO - 2010-2018

648258 / 224587

Oeschinensee 49 0.0402 1.11 56 ~ 1.6 1578 O ABO - 1983-2018

622116 / 149701

Soppensee 50 0.00286 0.25 27 ~ 3.1 596 E EGO - 2010-2018

648765 / 215720

Inkwilersee 51 0.00094 0.102 6 ~ 0.1 461 E# KOP - 2011-2018

617009 / 227527

Hüttwilersee 52 0.34 28 NA 434 E HAI - 2010-2018

705538 / 274275

Lake Cadagno 53 0.00242 0.26 21 ~ 1.5 1921 E PIO - 1981-2018

697683 / 156223

Lago Ritom* 54 0.048 1.49 69 NA 1850 O PIO - 1981-2018

695933 / 155169

Meteorological station Abreviation Altitude (m.a.s.l) Coordinates (CH)

Oberägeri AEG 724 688728 / 220956

Sattel SAG 790 690999 / 215145

Einsiedeln EIN 911 699983 / 221068

Mosen MOA 453 660128 / 232851

Cressier CRM 430 571163 / 210797

Altenrhein ARH 398 760382 / 261387

Güttingen GUT 440 738422 / 273963

Steckborn STK 397 715871 / 280916

Salen-Reutenen HAI 719 719099 / 279047

Interlaken INT 577 633023 / 169092

Thun THU 570 611201 / 177640

Pully PUY 456 540819 / 151510

Zürich / Fluntern SMA 556 685117 / 248066

Marsens MAS 715 571758 / 167317

Fribourg / Posieux GRA 651 575184 / 180076

Les Charbonnières CHB 1045 513821 / 169387

Bière BIE 684 515888 / 153210

Locarno / Monti OTL 367 704172 / 114342

Lugano LUG 273 717874 / 95884

Giswil GIH 471 657322 / 188976

Neuchâtel NEU 485 563087 / 205560

Egolzwil EGO 522 642913 / 225541

Luzern LUZ 454 665544 / 209850

Altdorf ALT 438 690180 / 193564

Gersau GES 521 682510 / 205572

Quinten QUI 419 734848 / 221278

Laschen / Galgenen LAC 468 707637 / 226334

Glarus GLA 517 723756 / 210568

Cham CHZ 443 677758 / 226878

Wädenswil WAE 485 693847 / 230744

Schmerikon SCM 408 713725 / 231533

Plaffeien PLF 1042 586825 / 177407

Segl-Maria SIA 1804 778575 / 144977

Blatten, Lötschental BLA 1538 629564 / 141084

Adelboden ABO 1322 609350 / 149001

Piotta PIO 990 695880 / 152265

B. Ice module The ice and snow module employed is based on the work of Leppäranta (2014, 2010) and Saloranta and Andersen (2007), and includes the following physical processes:

5 • Air temperature dependent formation and growth of black ice, including the insulating effect of a snow cover. • Snow layer build-up, including the compression effect due to the weight of fresh snow. • Buoyancy-driven formation of white ice. • Short wave irradiance reflection and penetration into the underlying water column. • Melting of snow, white and black ice due to both the direct heat flux through the atmospheric interface and the 10 absorption of short wave irradiance.

Three layers are used to represent black ice, white ice, and snow. An instant supply of water through cracks in the black ice is assumed to occur in order to form white ice. The water stored in ice and snow is neither withdrawn during ice formation nor added during melting to the water balance. Furthermore, the effect of liquid water pools on top of or between the layers is neglected 31

Below the freezing point (ice formation)

The ice module is activated as the water temperature in the topmost grid cell Tw (°C) drops below the freezing temperature

Tf (°C). Tf can be set to zero for a vertical grid size ≤ 0.5 m, the user can adapt (raise) this value to fit coarser grids. If

temperature is below the freezing point, the energy incorporated into the change of state Ef is calculated as

E= ρ c zT()− T 5 f w pw1 f w (B1)

-3 -1 -1 here ρw (1000 kg m ) is the density of fresh water, cpw the heat capacity of water (4182 J kg °C ) and z1 the height of the 5 -1 -3 topmost grid cell. Ef and the latent heat of freezing lh (3.34·10 J kg ) as well as the density of black ice ρib (916.2 kg m ) are

used for calculating the initial height of black ice hib (m) in Eq. B2, thereafter Tw is set equal to Tf

hEl= ( ρ ) ib f h ib (B2)

10 If an ice cover is present and if the atmospheric temperature Ta (°C) is smaller or equal to Tf, the growth of black ice dhib/dt continues as described in (Saloranta and Andersen, 2007).

dhib = 2ki(ρ ib ** l h) ( TT f - i ) dt (B3)

-1 -1 Here ki (2.22 W K m ) is the thermal conductivity of ice at 0 °C and Ti (°C) the ice temperature calculated as

PTfa+ T Ti = 1+ P (B4)

kh 1 P = maxis , kh10 h 15 s ib ib (B5)

-1 -1 There ks (0.2 W K m ) is the thermal conductivity of snow and hs (m) the height of the snow layer. When Ta is smaller than -1 the snow temperature (default set to 2 °C) water equivalent precipitation pr (m hour ) is turned into fresh snow hs_new (m) as

ρ hp= w s_ new r ρ s0 (B6)

-3 where ρs0 (250 kg m ) is the initial snow density. The existing snow cover hs (m) undergoes compression (first terms Eq. B7 20 and B8) by the new layer as described in Yen (1981), thereafter the new and existing layers are combined in both height and density (second terms of Eqs. B7 and B8).

dh ρ ss=−−hh1 + dt s [ρρ+ d ] s_ new ss (B7)

dρ − ρ ρρshh s+ s0_ s new s =ρρCwe C2 s −− ss1  s dt hs+ h s_ new  (B8)

-3 -3 here ρs (kg m ) is the snow layer density kept within ρs0 < ρs < ρsm with the maximum snow density set to 450 kg m , C1 (5.8 -1 -1 3 -1 m hour ) and C2 (0.021 m kg ) are snow compression constants, and ws (m) is the total weight above the layer under 5 compression expressed in water equivalent height.

-2 -2 If the snow mass ms (kg m ) becomes heavier than the upward acting buoyancy force Bi (kg m ), white ice with height hiw (m) -3 and density ρiw (875 kg m Saloranta, 2000) is formed between the snow and the black ice layers to achieve equilibrium

between Bi and ms.

Bh=(ρρ −+) h( ρρ −) i ib w ib iw w iw (B9)

dh m− B iw= s i dt ρ 10 s (B10)

In this model, we assume continuous supply of water through cracks in the black ice to form white ice. The formation of white ice takes place instantaneously each time step and we do not consider the influence of pools under the snow for melting or short wave irradiance penetration.

Above the freezing point (melting)

15 If an ice cover is present and if Ta > Tf melting starts. Each layer melts from above through the atmospheric interface and by penetrating short wave radiation

dh H x__ upper= − x y dt( l+ l ) ρ hex (B11)

-2 where Hx_y (W m ) is the layer-dependent heat flux (in the following, x represents s, iw or ib). The model supports melting through both sublimation (solid to gas) and non-sublimation (solid to liquid) with the inclusion/exclusion of the latent heat of -1 20 evaporation le (J kg ). Non-sublimation melting is default with le set to zero, for sublimation melting the user can set le to 2265 -1 kJ kg . For the uppermost layer (y = top, Eq. B12) the heat flux includes layer dependent uptake of short wave radiation Hs_x,

long wave absorption Ha or layer dependent emission Hw_x as well as sensible Hk and latent Hv heat. If the layer is not in direct

contact with the atmosphere, only Hs is used for melting from above (y = under, Eq. B13).

H= H ++ HH ++ HH xtopsxawxkv__ _ (B12)

HH= x__ under s x (B13)

5 Here we follow Leppäranta (2014, 2010) for determining the heat flux terms in Eq. B12. The transmittance of short wave

irradiance through each layer depends on each layers thickness hx as well as on the layer specific bulk attenuation coefficient -1 λx (m ; default λs = 24, λiw = 3 and λib = 2; Leppäranta, 2014).

(−λssh ) Hss_ = IA sp(1 −− A x) 1e  (B14)

(−λsh s) ( −− λλ s hh s iw iw ) Hs_ iw=−− IA s p(1e A x ) e  (B15)

(−−λλshh s iw iw) ( −− λλ s hh s iw iw − λ ib h ib ) Hs_ ib= IA s p(1e−− A x ) e 10  (B16)

(−−λλshh s iw iw − λ ib h ib ) Hsw_ = IA sp(1 −− A x) 1e  (B17)

-2 There Hs_w is the radiation penetrating through the ice cover to the water below and Is (W m ) the incoming short wave

irradiance. We introduce the albedo parameter Ap which tunes short wave irradiance in order to match observed water temperatures, thus adjusting the melting and indirectly the duration of the ice cover. Furthermore, depending on which layer

15 is in contact with the atmosphere we use a layer dependent constant albedo Ax (default As = 0.7, Aiw = 0.4 and Aib = 0.3; Leppäranta, 2014).

Ahss,0>  AAhx iw, s= 0& h iw > 0  Ah,0+= h  ib s iw (B18)

-1 Calculating Ha requires the long wave emission parameters ka = 0.68, kb = 0.036 (mbar ) and kc = 0.18 (Leppäranta, 2010), -8 -2 -4 atmospheric water vapour pressure ea (mbar), cloud cover C and Stefan Boltzmann’s constant σ (5.67*10 W m K ). For

20 Eqs. B19 and B20 the temperature Tx is given in Kelvin. Hw_x is layer dependent for the emissivity Ex with Eiw = Eib = 0.97 and -3 -3 Es(ρs) from 0.8 at ρs = 250 kg m to Es = 0.9 for ρs = 450 kg m . Calculating Hk and Hv requires the atmospheric density ρa = 34

-3 -1 -1 1.2 kg m , the heat capacity of air cpa = 1005 J kg K , the wind speed at 10 m height w10, the convective (bc) and latent (bl) bulk exchange coefficients both set to 0.0015 (Leppäranta, 2010; Gill, 1982), as well as the specific humidity both measured

qa (mbar) and at saturation q0. There qa = 0.622ea/pa where pa is the air pressure and q0 = 0.622*6.11/pa at Ta= 0 °C (Leppäranta, 2014).

24 Ha=++( k a k ba e1 kC c)σ T a 5  (B19)

H= ETσ 4 wx_ x f (B20)

Hk= ρ a c pa bT c( a− T f ) w10 (B21)

H=ρ lb( q − q) w v ah l a 0 10 (B22)

-2 As Hs_w warms the water under the ice, melting takes place from underneath with the energy Hbottom (W m ).

Hbottom=( T w − Tc f) pwρ w z1 10 (B23)

After obtaining Hbottom the temperature of the first cell is set to Tf and the decrease of ice cover from below becomes

dh H x_ lower = − bottom ρ dt lmx (B24)

Eq. B24 is only applied to hib and hiw. In principle, hs melts completely from above using Eq. B11 before hib and hiw reach zero,

however, if no ice is present, hs is set to zero. By combining Eqs. B11 and B24 the total melting of each ice layer is calculated 15 as

dh dh dh x =x__ lower + x upper dt dt dt (B25)

When hx < 0 due to melting the surplus energy is used for melting neighbouring layers according to the following procedure: if the melting is initiated from above the surplus energy is used to melt the layer directly underneath; if the melting is caused

by the water below the layer directly above receives the surplus melting energy; if hib <= hiw <= 0 the water in the topmost grid 20 cell is heated with the remaining energy.

Ice model performance

To test the ice module, Simstrat was calibrated in Sihlsee with PEST using monthly resolved vertical temperature profiles (2006 to 2008, RMSE 1.2 °C) for four parameters including the new p_albedo parameter for scaling snow/ice albedo. Modelled and monthly measured total ice cover from 2012 to 2018 is shown in Fig. B1 (RMSE 0.078 m). The modelled thickness agrees well with measurements during years with an extensive ice covered period (2013, 2014 and 2017, max height > 5 cm). The 5 model performance is not ideal for years with short temporal ice duration and thin ice thickness (2016 and 2018, max height < 5 cm). During these years, the quality of the forcing dataset becomes crucial. In the case of Sihlsee, the timing and duration of snowfall prolongs the duration of the ice-covered period. We use the meteorological station at Samedan (SAM) located four kilometres from the lake in a region with rapid topographical change. This in combination with monthly ice thickness measurements result in the divergence during 2016 and 2018.

Figure B1. Ice model performance in Sihlsee (2012 to 2018) showing modelled white ice (orange), black ice (green) and total ice cover (white- and black ice combined, in blue) against measurements (black).

C. Estimation of clear-sky solar radiation The algorithm below is based on the equations from the Lake HeatFluxAnalyzer (see http://heatfluxanalyzer.gleon.org/), following the methods of Meyers and Dale (1983).

Declination of the sun [rad]: = sin ( 0.39779 cos ), where DOY is the day of year after the winter solstice . −1 2𝜋𝜋DOYs 5 (December 21st). 𝛿𝛿 − 365 24 s

( . ) Cosine of the solar zenith angle [-]: cos = max(sin sin + cos cos cos , 0), where is the latitude in 𝜋𝜋 H−12 5 radians and H is the hour of the day, assuming𝑍𝑍 the solarφ noon𝛿𝛿 is at 12h30.φ 𝛿𝛿 12 φ

Air mass thickness coefficient [-]: = 35 cos (1244 cos + 1) . 2 −0 5 Dew point temperature [°C]: =𝑚𝑚243.5 log 𝑍𝑍 /(17.67 𝑍𝑍log ) + 33.8, where [mbar] is the water vapour pressure. . . 𝑝𝑝𝑤𝑤 𝑝𝑝𝑤𝑤 𝑇𝑇𝑑𝑑 6 112 − 6 112 𝑝𝑝𝑤𝑤 10 Precipitable water vapour [cm]: = . ( ) . ( . ), where is an empirical constant dependent on latitude 0 1133−log 𝐺𝐺+1 +0 0393 1 8 𝑇𝑇𝑑𝑑+32 and day of year (see tables from𝑤𝑤 Smith,𝑝𝑝 𝑒𝑒 1966). 𝐺𝐺

Attenuation coefficient for water vapour [-]: = 1 0.077 ( ) . 0 3 𝑤𝑤 𝑝𝑝 Attenuation coefficient for aerosols [-]: =𝜆𝜆0.935 − 𝑤𝑤 𝑚𝑚 𝑚𝑚 𝑎𝑎 Attenuation coefficient for Rayleigh scattering𝜆𝜆 and permanent gases [-]: = 1.021 0.084( (0.000949 + 0.051)) . , 0 5 15 where [mbar] is the air pressure. 𝜆𝜆𝑅𝑅𝑅𝑅 − 𝑚𝑚 𝑝𝑝𝑎𝑎 𝑎𝑎 Effective𝑝𝑝 solar constant [W m-2]: = 1353(1 + 0.034cos ), where DOY is the day of year. . 2𝜋𝜋DOY 𝐼𝐼eff 365 24 Clear-sky solar radiation [W m-2]: = cos

cs eff 𝑤𝑤 𝑎𝑎 𝑅𝑅𝑅𝑅 𝐻𝐻 𝐼𝐼 ∙ 𝑍𝑍 ∙ 𝜆𝜆 𝜆𝜆 𝜆𝜆